Narrow Results

Starting from the classical nonrelativistic electrodynamics in 1+1 dimensions, a higher-derivative version is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of the original electrodynamics, preserving its gauge invariance. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization for the higher-derivative model is developed. By extending the Faddeev–Senjanovic algorithm, the path integral quantization is carried out. Hence, the Feynman rules are established and the diagrammatic structure is analyzed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams of the original model, where the electromagnetic field propagator is present. A generalization of the BRST quantization is also considered.

In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory constructions, and we found exact solutions in the low frequency, low momentum limit (ω, k ≪ T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1 + 1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.